so in a nutshell _ 1/(1-0.9)=infinity 1/infinity=0 therefore _ 1-0.9 = 0 ? it's certainly not intuitive but i think it is true. also seems pretty academic for practical purposes. it would be interesting to look at this thread (well the rounding thread) from a point of view of how many siginificant digits do i need so that i'm not significantly biasing my calculations ie: my robot won't be off course more than a 1" after traveling 20' using my optical encoder or accelerometer or whatever. is anybody still reading this thread? :) -pete On Mon, 4 Jun 2001, Jeff DeMaagd wrote: > ----- Original Message ----- > From: David VanHorn > > > > Perhaps you could look at it in this casual, common-sense way: > > > > > > If 0.999... APPROACHES 1 as the number of 9s APPROACHES infinity, > > > > Ok > > > > > then 0.999... EQUALS 1 when the number of 9s EQUALS infinity. > > > > No. > > I see no requirement that it do so. > > > > > Feynman hasn't been having trouble with ANY calculations since > > > he died, and if Hawking could speak, I'm pretty sure he'd tell > > > you that 0.999... is equal to 1. > > > > For any practical matter, yes. > > However, in an absolute sense, this is just sweeping some ugliness under > > the carpet. > > I haven't seen this used in this thread, so I'll describe it this way, as my > old college calc prof used this as his example, try this: > > Using decimal representations: > 1/3 = .33333333333 (to infinity) > > 1/3 * 3 = .3333333333 * 3 = .99999999999 (to infinity) > > However, using fracional simplification: > 1/3 * 3 = 3/3 = 1/1 = 1 > > Therefore 1 = .9999999999 (to infinity) > > Is that good enough for you? > > > If you can't represent it, then you can't do calculations with it. > > What is wrong with the overbar? Are you requiring all numeric > representations be in decimal? So I can't use Pi in any of my calculations? > e? i? > > Jeff > -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email listserv@mitvma.mit.edu with SET PICList DIGEST in the body